05 mm wacc

FIN 591: Financial Fundamentals/Valuation 2
M&M: The Starting Point
 A number of rest r ict ive assumpt ions apply
 Use t he addit ivit y pr inciple
 Derive proposit ions re: valuat ion and cost
of capit al
 Derived in bot h t he “no t ax” and “t ax” cases.

The M&M Assumptions
 Homogeneous expect at ions
 Homogeneous business r isk (σEBI T) classes
 Per pet ual no-growt h cash f lows
 Per f ect capit al market s:
 Perf ect compet it ion; i.e., everyone is a price
t aker
 Firms and invest ors borrow and lend at t he
same rat e
 Equal access t o all relevant inf ormat ion
 No t ransact ion cost s (no t axes or bankrupt cy
cost s).

Business Risk
 Business r isk:
 Risk surrounding expect ed operat ing cash f lows
 Fact ors causing high business r isk:
 High correlat ion bet ween t he f irm and t he
economy
 Firm has small market share in compet it ive market
 Firm is small relat ive t o compet it ors
 Firm is not well diversif ied
 Firm has high f ixed operat ing cost s.

Principle of Additivity
 Allows you t o value t he cash f lows in any
way t hat you like
 Eit her value each individual component at it s
own risk adj ust ed discount rat e (RADR)
 Or value t he sum of t he component s at t he
RADR t hat is appropriat e t o t he sum
 The concept :
PV[A+ BatRADRappropriateto(A+ B)]
= PV(AatRADRappropriatetoA)
+ PV(BatRADRappropriatetoB).

Additivity Example
Mar ket risk pr emium = 8%; r isk-f ree rat e =
6%
RADR of A = 6% + 1 * 8% = 14%
RADR of B = 6% + 2 * 8% = 22%
Value of A = $100 / 1.14 = $87.72
Value of B = $150 / 1.22 = $122.95
Port f olio = $87.72 + $122.95 = $210.67
Asset
1-Period
E(payoff) Beta
A $100 1
B $150 2

M&M Capital Structure
Propositions (No Taxes)
 M&MPropositionI:
Value of unlevered f irm = value of levered f irm
 M&MPropositionII:
r e = ru + (ru - r b) B / S
r b = cost of debt
r e = cost of equit y
r u = cost of capit al f or all-equit y f irms in t his risk class
B = value of debt
S = value of st ock or equit y.
Also, defined as
return on assets

M&M Propositions I & II
(No Taxes)
Investment Alternative I nit ial invest ment = $5,000
EBI T = $1,000 f orever
r u = 10%
= Required ret urn on unlevered
equit y
Financing Alternatives
Unlevered Levered
Equit y $5,000 $4,000
Debt (r b = 5%) $1,000
Cash Flows
EBI T $1,000 $1,000
– I nt erest –50 = (.05)1,000
EBT 1,000 950
– Tax (0%)
Net income 1,000 950
→ Cash f lows debt + equit y $1,000 $1,000

(No Taxes)
 PropositionI: VL = VU
VU = S = (EBI T) / r u = $1,000 / .1 = $10,000
VL = B + S = [I nt + (EBI T - I nt )] / r u = $1,000 / .1 = $10,000
⇒ S = VL – B = $10,000 – $1,000 = $9,000
⇒ Capit al st ruct ure: ir relevant wit hout corporat e t axes
 PropositionII: re = ru + (B/S)(ru – rb)
ru = .10 + ($0 / $10,000) (.10 – .05) = 10%
re = .10 + ($1,000 / $9,000) (.10 – .05) = 10.556%
 WACC = 10.556% * 90% + 5% * 10% = 10%.

Graphing the M&M No- Tax
Relationships
Firm value (Proposit ion I )
VU VL
Debt
Required ret urn on equit y (Proposit ion I I )
r e
Slope = (r u – rb )
r u WACC
Debt / equit y

M&M Capital Structure
Propositions (Corporate Taxes)
 M&MPropositionI:
VL = VU + τ C B
 M&MPropositionII:
re = r u + (B / S) (1 – τc ) (r u – r b)
wher e
τc= Cor porat e t ax r at e
Ot her var iables are as pr eviously def ined.

(Corporate Taxes)
I nvest ment and f inancing alt ernat ives - same as
bef ore
Af t er-t ax cost of capit al f or unlevered f irm r u = 10%; τC =
34%
Cash Flows Unlevered Levered
EBI T $1,000 $1,000
– I nt erest –50 =
(.05)1,000
EBT 1,000 950
– Tax (34%) – 340 – 323
Net income 660 627
→ Cash f low debt + equit y $ 660 $ 677
$17 difference = $50 interest x 34% tax rate

Tax Benefit of Debt
Financing Debt int er est is t ax deduct ible
 For ever y $1 of int er est expense:
 Company pays $1 * (1 - τ)
 Government pays $1 * τ
 Example:
I ncome t ax savings = I nt erest expense * τ
= $50 * .34 = $17
 PV of gov’t subsidy adds value t o st ock
PV t ax savings = I ncome t ax savings / market rat e
= $17 / .05 = $340.

A Look at the Propositions
 PropositionI: VL = VU+ τCB
VU = EBI T (1 – τC) / r u = $660 / .1 = $6,600
VL = VU + τ CB = $6,600 + $340 = $6,940
⇒ S = VL – B = $5,940.
 PropositionII: re = ru + (B/S)(1 – τc)(ru – rb)
ru = .10 + ($0 / $6,600) (1–.34) (.10 – .05) = 10%
re = .10 + ($1,000 / $5,940) (1 – .34) (.10 – .05) = 10.556%
WACC = (B / VL ) (1 – τc ) rb + (S / VL ) re
= ($1,000 / $6,940) (1 – .34) (.05)
+ ($5,940 / $6,940) (.10556) = 9.51%.

Confirmation
VL = B + S
= r b B / r b + (EBI T – r d B) (1 – τc) / r e
= $50 / .05 + ($1,000 – $50) (1 – .34) / .
10556
= $1,000 + $5,940 = $6,940
VL = EBI T (1 –τc) / WACC = $660 / .0951
= $6,940.

Graphing the M&M
Relationships
Firm value (Proposit ion I )
VL
Slope = τc
VU
Debt
Required ret urn on equit y (Proposit ion I I ) r e
Slope = (1 – τc )(ru – rb )
ru WACC
rb
Debt / equit y

Another Look
with Corporate Taxes
Market Value Balance Sheet (All equity firm)
Physical asset s = $1,000(1 – .34)/ (.1) Equit y = $6,600
= $6,600 (1,000 shar es at $6.60)
Market Value Balance Sheet (Upon announcement of debt issue)
Physical asset s $6,600 Equit y = $6,940
(1,000 shar es at $6.94)
Pr esent value of t ax shield = TCB
= (.34) ($1,000) = $340
Tot al asset s = $6,940
Market Value Balance Sheet (After exchange has taken place)
Physical asset s $6,600 Equit y = $5,940
(855.91 shar es at $6.94)
Pr esent value of t ax shield = TCB
= (.34) ($1,000) = $340 Debt = $1,000
Tot al asset s = $6,940 Debt plus equit y
= $6,940

An Aside:
Introducing Personal Taxes
 Miller (1977) suggest s t hat debt has bot h
t ax advant ages and disadvant ages
 Advantages derive f rom t he t ax deduct ibilit y of
int erest at t he corporat e level
 Disadvantages because personal t axes levied on
int erest income usually exceed t hose levied on
equit y income

Why?
 Easy t o def er equit y income
 Non-dividend paying st ocks
 Push capit al gains int o t he f ut ure
 What is t he ef f ect on f ir m value?

Miller’s Argument
 VL = VU + [1 - (1 - τc)(1 - τs) / (1 - τb)] B
 I f (1 - τc) (1 - τs) / (1 - τb) >1
 I t is less cost ly t o pay t he dollar t o
shareholders t han t o debt holders

Assume a const ant corporat e income t ax rat e

Need τs < τb
 I f (1 - τc) (1 - τs) / (1 - τb) <1
 I t is more cost ly t o pay t he dollar t o
shareholders t han t o debt holders.

Net Tax Advantage
 PV of net t ax advant age (NTA) of per pet ual
debt :
NTA = 1 - (1 - τc)(1 - τs) / (1 - τb)
 How lar ge is t he net t ax ef f ect of debt ?
 Assume: τc = 34%; τs = 28%; τb = 39.5%
 NTA= 1 - (1 - .34)(1 - .28) / (1 - .395) = 21.45%
 I f τs = τb, t he NTA = _____
 Conclusion:
 Debt may have less impact t han t he M&M posit ion.

Changing the Rates
 Suppose shar eholder s can def er t axes,
t her eby lower ing t he ef f ect ive r at e f rom
28% t o 15%
 NTA = 1 - (1 - τc)(1 - τs) / (1 - τb)
 Then NTA = 7.3%
 Suppose τc = 27.2%, τs = 15%, τb = 39.5%
 Then NTA = -2.3%
 Empir ical evidence suggest s t hat NTA <τc.

How Does NTA
Affect M&M Model?
 M&M:
VL = VU + τc B
 Miller:
VL = VU + [1 - (1 - τc)(1 - τs) / (1 - τb)] B
 I f τs = τb in t he Miller model, t hen t he
Miller model r educes t o t he M&M model.

A Graphical View of Miller
Value
Vu
Debt (B)
VL = VU + TcB when TS = TB
VL = VU + [1 - (1 - Tc)(1 - TS)/(1 - TB)]B
when (1 - TB) > (1 - Tc)(1 - TS)
VL = VU when (1 - TB) = (1 - Tc)(1 - TS)
VL < VU when (1 - TB) < (1 - Tc)(1 - TS)
Tc = corporate tax rate
TB = personal tax rate on interest
TS = personal tax rate on dividends & other equity distributions.

Relationship Between
Firm Value and WACC
 Value of f irm = Value of debt + value of equit y
 ∆(Value) / ∆(I nvest ment )
= Marginal cost of capit al t o maint ain f irm value
 ∆V / ∆I = r u (1 - τcdB / dI ) = WACC
 See slide#14
WACC = r u (1 - τc B / S)
= .10 (1 - .34 * 1000 / 6940) = 9.51%
 Derive WACC f rom f irm value — not vice versa
 Earnings perspect ive
 Financing perspect ive.
Assumes
τs = τb

WACC: An Earning Power
View
 Assumpt ions:
 Maint ain current level of product ion and ef f iciency
 All cash f lows paid as dividends t o shareholders
 WACC
= Const ant cash operat ing prof it s * (1 - τc)
Market value of unleveredf irm
= $660 / $6,600 = 10% (see slide#9)
 WACC
= Const ant cash operat ing prof it s * (1 - τc)
Market value of leveredf irm
= $660 / $6,940 = 9.51% (see slide#14).

WACC: A Financing View
 Calculat e t he cost of :
 Debt
 Pref erred st ock
 Common st ock
 Combine t he dif f erent f orms of capit al
int o a weight ed average cost of capit al —
WACC.

Debt’s Yield to Maturity
Example: 14s of December 2014 selling f or 110 on J uly 1, 2003
$1000
$70 $70 $70 $70
$70 $70
6/ 97 12/ 97 6/ 98 12/ 98 12/ 07
6/ 08 12/ 08
$1,100 = $70/ (1 + r) + $70/ (1 + r)2
+ $70/ (1 +r)3
+ …+$1,070/ (1 + r)23
where ris a semiannual rat e of int erest
Find t he YTM?
At r = 0%, PV = ($70)(23) + $1,000 = $2,610
At r= I nf init y, PV = $0
. . .
How much is the coupon
rate?
Is r greater than the
coupon rate? Less than?
Equal to?

A Graphical View: YTM
Semiannual interest rate (r)
$2,610
$2,000
$1,100
$1,000
1 2 3 4 5 6 7 8 9
…
PV
6.17

Cost of Debt
 Cost of debt t o t he f ir m is t he YTM t o
invest or s adj ust ed f or corporat e t axes
 Cost of debt = YTM * (1 - τc)
 Example:
A f ir m’s debt t rades in t he market t o
pr ovide a YTM of 5%. I f t he f ir m’s t ax r at e
is 34%, how much is t he af t er -t ax cost of
debt ?
Answer : 5% * (1 - .34) = 3.30%.

Cost of Debt = YTM * (1 -
τc)
 Represent s a good approximat ion if
shareholders don’t def ault on debt
service obligat ions
 I t is t he rat e shar eholder s promise t he debt
holders
 Thus, bondholder s’ expect ed ret ur n <
YTM
 See Exhibit 10.1, page 211 of t ext .

Cost of Preferred Stock
 Pref er red st ock dividend is not t ax
deduct ible
 Cost is t he market r et urn ear ned by
invest or s:
Dividend / market price of pref erred st ock
 Example:
A pr ef err ed st ock (par = $20) pays a $3
dividend annually. I t curr ent ly t r ades in
t he mar ket f or $24. How much is t he cost
of t he st ock f r om t he f irm’s per spect ive?
Answer: $3 / $24 = 12.5%.

Cost of Equity
 Cost of equit y is mor e dif f icult t o calculat e
t han eit her t he cost of debt or t he cost of
pr ef err ed st ock
 Met hods commonly used:
 M&M model
 Dividend growt h model (Gordon model)
 I nvert ed price-earnings rat io
 Securit y market line
 Build-up approach.

Using Historic Returns
 Est imat ing cost of capit al using past
r et ur ns is j ust if ied by “rationalexpectations” t heory
 I nvest ors’ expect at ions f or ret urns t hat
compensat e t hem f or risk can’t be
syst emat ically of f t arget
 The average of past ret urns is t he ret urn
t hat invest ors expect t o receive

Somet imes t he ret urn is higher; ot her
t imes lower

However, errors are not syst emat ic.

Dividend Growth Model
r e = D1 / P0 + g = D0 (1 + g) / P0 + g
 Assumes t he t erm st r uct ure of RADR is
f lat
 Dividends grow at expect ed r at e g in
perpet uit y
 g represent s sust ainable growt h
 Use average or geomet ric rat e?
 Use real or nominal dividend growt h?
1 + r r eal = (1 + r nominal) / (1 + inf lat ion)

Growth Rate
 Arit hmet ic ret ur n:
 Simple average of hist orical ret urns
 Geomet r ic ret ur n:
 [(1 + r 1)(1 + r2) …(1 + r n)]1/n
- 1
 Wit h hist or ical dat a, t he arit hmet ic
aver age:
 Provides expect ed annual ret urn as a draw f rom
t he dist ribut ion of possible annual ret urns
 Geomet ric average is an est imat e of compound
rat e of ret urn

Downward bias est imat e of t he average ret urn.

Equity Cost Using the
Dividend Growth Model
 Price = Expect ed dividend next year .
Required mar ket rat e - gr owt h r at e
Rearrange:
Required mar ket rat e = D1/ P0 + g
 Example:
A f ir m’s st ock curr ent ly sells f or $25 per
share. The f or ecast f or next year ’s
dividend is $1 and t his dividend is expect ed
t o grow 10% annually.
Answer: $1 / $25 + .10 = .14 or 14%.

P/E and Cost of Equity
 Dividend gr owt h model:
r e = D1 / P0 + g
 Assume:
 Firm has a f ixed dividend payout policy, b
 Earnings grow at a f ixed rat e, g
 Revised dividend gr owt h model:
re = D1 / P0 + g = b * EPS1 / P0 + g
= b * EPS0 (1 + g) / P0 + g = [b (1 + g) / PE0] + g.

Problem with Dividend
Model
 Says not hing about risk!
 Ret urns should be based on perceived
risk
 But not t ot al risk
 I nvest ors able t o diver sif y away some
risk
 Market only compensat es f or non-
diver sif iable or syst emat ic r isk.

The End

05 mm wacc

Recommended

Recommended

More Related Content

What's hot

What's hot (19)

Similar to 05 mm wacc

Similar to 05 mm wacc (20)

05 mm wacc